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Wikipedia provides an updated browser statistics summary that includes the top sources and median of these sources:
http://en.wikipedia.org/wiki/Usage_share_of_web_browsers#Summary_table
For most uses, the wikipedia median is probably your best estimate for accurate browser statistics.
Each of the main browser stats providers are not 100% reliable ...

Google Analytics is pretty much the best around, regardless of server platform. Unless there is a specific reason you need to use server-side analytics rather than a client-side Javascript solution, Google Analytics is the way to go.

http://en.wikipedia.org/wiki/Usage_share_of_web_browsers
This page list the best and most reliable source of information on the market share of browser. Pretty much everything that people will answer is listed there.
Here's the list :
W3Counter : http://www.w3counter.com/globalstats.php
Net Applications : ...

As explained in part by Google's "Why don't my web logs or third-party click auditing software match my AdWords report?" support article, Google AdWords and Google Analytics do not track traffic in the same way that WordPress or your web server logs will report.
Your host may be presenting you with data for all requests, including JavaScript files, CSS ...

Practically zero. Because:
The vast majority of users don't type in URLs anymore. They type the company name / domain name into a Google search box in the browser chrome, and go to the first result Google returns.
If users expect to revisit your site often, they'll bookmark it.
Update: I'll add a bit based on the good comments and answers given by others ...

Google Analytics and Alexa have nothing to do with one another.
Alexa is a relatively meaningless metric which only shows an approximate traffic rank based on only users that have their browser toolbar/extension/site script installed. It can only measure statistics based on their own userbase so the real accuracy of Alexa ranking is considerably wayward.
...

A lot of great resources listed in the answers so far, great question.
To me, the only reliable source of data you should look at for browser usage, and thus, what you need make sure you're supporting well, is your own site. Keep an eye on those breakdowns and you'll have a sense of your actual audience. If you get spikes in traffic because of news or ...

Due to the design/nature of the Internet such figures are really hard/impossible to obtain. There will be a lot of variance between countries/regions in countries in regards to time spent online, and which hours are spent online.
Also definitions of Internet access are a little difficult to pin down. Is someone sending an email on their phone on the ...

I don't have any data that directly correlates page speed with click thrus. However, this article shows how important page speed is in a variety of other areas and may be useful to you:
Amazon: 100 ms delay caused a drop in revenue.
Google: 400 ms delay caused a 0.59% decrease in search requests per
user.
Yahoo!: 400 ms delay caused a 5-9% ...

Follow the KISSMetrics guide
The KISSMetrics blog has a detailed post titled, “How to (Finally) Make Web Analytics Work for You” that explains the process of evaluating exactly what's worth tracking. It breaks it down into the following steps:
Identify business objectives.
Specify website goals.
Distinguish website Key Performance Indicators.
Visitor ...

Why not use Google Analytics? It is the better way to view your traffic without a lot of scripts. You can make your account in seconds and only install some lines of code in your file (index).
http://www.google.com/analytics/

Google Analytics can be used with single page applications. You can either use Events to track user behaviour, or you can register "virtual" page views in the same way that real pages get recorded in a multi-page site.

Many competitive research tools (e.g. compete.com) show estimates for site traffic, but their reliability is questionable. There's no definitive way to determine a website's traffic without access to logs and detailed analytics. I think sites that sell advertising through AdSense have their traffic statistics tracked by Google, and some competitive research ...

Use the "Navigation Summary" to work out which internal page a visitor reached your page from:
Choose 'Content' and then 'Content by Title' from the Analytics menu:
Click whichever page title you're interesting in learning more about:
Click the page URL in the Content Performance table:
Click 'Navigation Summary' under the 'Navigation Analysis' ...

They'll get the IP, user agent and cookies from your users. If you're worried about using hosted analytics, you can look at hosting a program on your own servers to gather analytics such as Open Web Analytics.

If he has logs of his server traffic then all the information you need is in there, almost everything google analytics does can be pulled out of server logs (and more, there are some things like 404/500 error codes that GA cannot track).
This was how analytics was done prior to page tagging. Google used to offer an updated version of the Urchin 5 log ...

Providing initial explanation re difference between server-side stats and online stats for the benefit of other users:
Apache access log analyses all the traffic to your server.
StatCounter tracks all the visits to your site.
Your server gets a lot more traffic than your site, because server traffic includes all the visits from robots, spambots, crawlers ...

I know that referrer field can be changed.. but why?
This is known as referrer spam - unfortunately, spammers caught on to the fact that some webmasters do not secure their automatically-generated stat reports and, as most report generators do not add nofollow to referrer links, it is possible to get a link from a number of domains simply by providing a ...

It depends on the type of redirect. If you have a Javascript or Meta Refresh redirect with Google Analytics running on that page, then Google might track the page if the pause between loading the page, loading the Google Analytics tracking script and the redirect is long enough.
If you have a server redirect, then no Javascript code is actually triggered ...

No, unfortunately it's not literally 100,000 different people. More accurately, it's 100,000 different cookie values. A user can visit your site for the very first time and be counted with a first unique visit, but if they clear their cookies, or log in from a different computer, or do private browsing, then a subsequent visit would be "unique" again. So ...

Using campaign variables, you can tag the contents of links in your advertisements. This will let you track the inbound performance of your advertising.
So, if you have a banner ad on Reddit for example.com/reddit-sale, you could use the link with something like.
...

Try Analog or Awstat.
Another solution is Pion Core. This is the open source edition of the Pion analytics platform. However, it's more of a general-purpose analytics platform (which includes packet sniffing analytics), not just a log analyzer. It has log analyzing capabilities though.

US federal law pertaining to Fraud and related activity in connection with computers suggests that it is unlawful to:
intentionally access a computer
without authorization or exceeds
authorized access, and thereby obtain
information contained in a financial
record of a financial institution, or
of a card issuer as defined in section
1602 ...

You could keep track of number of downloads per file simply by feeding the file through a server side script in the language of your choosing as opposed to linking directly to the file. By doing it this way every time the file is requested you can log it, and information about who is downloading it, in a database. See this answer for an example of this in ...